Topological Excitons and Their Superfluid Phase in Flat Chern Bands

Excitons are the neutral bosonic quasiparticles that form when Coulomb interactions create bound states between electrons and holes. In interacting Chern insulators, excitons may inherit the nontrivial topology and quantum geometry from the underlying electron wavefunctions. We theoretically investigate excitonic bound states, their midgap bands, and superfluidity in flat-band Chern insulators pumped with light. We predict that the exciton wavefunctions will exhibit vortex structures in momentum space, with the total vorticity being equal to the difference of Chern numbers between the conduction and valence bands. Both the exciton binding energy and the exciton superfluid density are proportional to the Brillouin-zone average of the quantum metric and the Coulomb potential energy per unit cell. Optical selection rules of topological excitons are dominated by both quantum-geometry and topological constraints. Spontaneous emission of circularly polarized light from radiative decay is a detectable signature of the exciton vorticity. After addressing the existence of topological excitons and their experimental signatures both in the normal and superfluid phases, we show that exciton bands, set by their center of mass momentum, have finite Chern numbers with corresponding excitonic edge states. We propose that topological excitons and their superfluid phase could be realized in flat bands of twisted Van der Waals heterostructures.